Question: Consider the complex vector space \[{{\mathbb{C}}^{2}}=\left\{ \left( {{z}_{1}},{{z}_{2}} \right):\,\,{{z}_{1}},{{z}_{2}}\in \mathbb{C} \right\}\] . For each element \[\left( {{z}_{1}},{{z}_{2}} \right)\in {{\mathbb{C}}^{2}}\] find complex numbers \[\alpha \] and \(\beta \) for which

Do \(\left( 1+i,1-i \right)\) and \(\left( 2+i,2-i \right)\) form a linearly independent pair in \({{\mathbb{C}}^{2}}\) ? Do \(\left( 1+i,1-i \right)\) and \(\left( 2+i,2-i \right)\) span \({{\mathbb{C}}^{2}}\) ?

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